Template:Langle/doc
This is the left-handed angular bracket used for writing averages or bra-ket notation, with other applications primarily in mathematics and physics, for use when inline html rendering is desired rather than Template:TeX rendering.
Examples
There is no need to use spaces around the template, due the large spacing in the template glyph.
- Examples of bras
The superposition of states can be written ⟨p| +⟨q| +⟨χ| +⟨ψ|, which is inline with the text.
Another superposition of states: ⟨P| +⟨Q| +⟨Φ| +⟨Ψ|, again inline.
The superposition of states can be written {{langle}}p| +{{langle}}q| +{{langle}}χ| +{{langle}}ψ|, which is inline with the text.
Another superposition of states: {{langle}}P| +{{langle}}Q| +{{langle}}Φ| +{{langle}}Ψ|, again inline.
- In conjunction with {{Rangle}}
One sum of inner products is ⟨p|qTemplate:Rangle+⟨χ|ψTemplate:Rangle, a real number.
Another sum of inner products is ⟨P|QTemplate:Rangle+⟨Φ|ΨTemplate:Rangle, another real number.
{{langle}}p|q{{rangle}}+{{langle}}χ|ψ{{rangle}}
{{langle}}P|Q{{rangle}}+{{langle}}Φ|Ψ{{rangle}}
The average of a quantity q may be written ⟨qTemplate:Rangle. The root mean square is then √⟨q2Template:Rangle, i.e. square every value, then average, then take the root.
The average of a quantity ''q'' may be written {{langle}}''q''{{rangle}}. The root mean square is
then √{{langle}}''q''<sup>2</sup>{{rangle}}, i.e. square every value, then average, then take the root.
See also
For use with {{Rangle}}